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Zap. Nauchn. Sem. POMI, 2010, Volume 378, Pages 58–72 (Mi znsl3828)  

This article is cited in 6 scientific papers (total in 6 papers)

Asymptotic behavior of the scaling entropy of the Pascal adic transformation

A. A. Lodkin, I. E. Manaev, A. R. Minabutdinov

Saint-Petersburg State University, Saint-Petersburg, Russia

Abstract: In this paper, we give an estimation for the growth of the scaling sequence of the Pascal adic transformation with respect to the $\sup$-metric. We construct a special class of $\alpha$-names of positive cumulative measure. The linear growth of its cardinality implies the logarithmic growth of the scaling sequence. Bibl. 14 titles.

Key words and phrases: Pascal adic transformation, scaling sequence, entropy.

Full text: PDF file (854 kB)
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English version:
Journal of Mathematical Sciences (New York), 2011, 174:1, 28–35

UDC: 517.987.5
Received: 09.10.2010

Citation: A. A. Lodkin, I. E. Manaev, A. R. Minabutdinov, “Asymptotic behavior of the scaling entropy of the Pascal adic transformation”, Representation theory, dynamical systems, combinatorial methods. Part XVIII, Zap. Nauchn. Sem. POMI, 378, POMI, St. Petersburg, 2010, 58–72; J. Math. Sci. (N. Y.), 174:1 (2011), 28–35

Citation in format AMSBIB
\Bibitem{LodManMin10}
\by A.~A.~Lodkin, I.~E.~Manaev, A.~R.~Minabutdinov
\paper Asymptotic behavior of the scaling entropy of the Pascal adic transformation
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XVIII
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 378
\pages 58--72
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3828}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 174
\issue 1
\pages 28--35
\crossref{https://doi.org/10.1007/s10958-011-0278-x}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952814585}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Vershik, “Scailing entropy and automorphisms with pure pointspectrum”, St. Petersburg Math. J., 23:1 (2012), 75–91  mathnet  crossref  mathscinet  zmath  isi  elib
    2. A. M. Vershik, “The Pascal automorphism has a continuous spectrum”, Funct. Anal. Appl., 45:3 (2011), 173–186  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. A. A. Lodkin, I. E. Manaev, A. R. Minabutdinov, “A realization of the Pascal automorphism in the concatenation graph, and the function $s_2(n)$”, J. Math. Sci. (N. Y.), 190:3 (2013), 459–463  mathnet  crossref  mathscinet
    4. A. R. Minabutdinov, I. E. Manaev, “The Kruskal–Katona function, Conway sequence, Takagi curve, and Pascal adic”, J. Math. Sci. (N. Y.), 196:2 (2014), 192–198  mathnet  crossref  mathscinet
    5. A. R. Minabutdinov, “Random deviations of ergodic sums for the Pascal adic transformation in the case of the Lebesgue measure”, J. Math. Sci. (N. Y.), 209:6 (2015), 953–978  mathnet  crossref
    6. A. A. Lodkin, A. R. Minabutdinov, “Limiting curves for the Pascal adic transformation”, J. Math. Sci. (N. Y.), 216:1 (2016), 94–119  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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